Homework Help is Here – Start Your Trial Now!
Math
Calculus
. Sketch a graph of a function f that is continuous ón (-0, 0 such thát f'(x)Ó on Eo,o); f'(x) < O and f"(x) < o on (0,00)

. Sketch a graph of a function f that is continuous ón (-0, 0 such thát f'(x)Ó on Eo,o); f'(x) < O and f"(x) < o on (0,00)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
**Question** Sketch a graph of a function \( f \) that is continuous on \((-\infty, \infty)\) such that: - \(f'(x) < 0\) and \(f''(x) > 0\) on \((-\infty, 0)\); - \(f'(x) < 0\) and \(f''(x) < 0\) on \((0, \infty)\). **Explanation** Given these conditions: 1. **On the interval \((-\infty, 0)\):** - \(f'(x) < 0\) indicates that the function \( f(x) \) is decreasing. - \(f''(x) > 0\) means that the function is concave up (the slope is increasing). 2. **On the interval \((0, \infty)\):** - \(f'(x) < 0\) indicates that the function \( f(x) \) is decreasing. - \(f''(x) < 0\) means that the function is concave down (the slope is decreasing). The graph of such a function would show a continuous curve that decreases as it moves from left to right across the entire number line, with a change in concavity at \(x = 0\). On the left side of the y-axis, the curve would start decreasing but concaving upwards, and on the right side, it would continue to decrease but now concaving downwards.
Transcribed Image Text:**Question** Sketch a graph of a function \( f \) that is continuous on \((-\infty, \infty)\) such that: - \(f'(x) < 0\) and \(f''(x) > 0\) on \((-\infty, 0)\); - \(f'(x) < 0\) and \(f''(x) < 0\) on \((0, \infty)\). **Explanation** Given these conditions: 1. **On the interval \((-\infty, 0)\):** - \(f'(x) < 0\) indicates that the function \( f(x) \) is decreasing. - \(f''(x) > 0\) means that the function is concave up (the slope is increasing). 2. **On the interval \((0, \infty)\):** - \(f'(x) < 0\) indicates that the function \( f(x) \) is decreasing. - \(f''(x) < 0\) means that the function is concave down (the slope is decreasing). The graph of such a function would show a continuous curve that decreases as it moves from left to right across the entire number line, with a change in concavity at \(x = 0\). On the left side of the y-axis, the curve would start decreasing but concaving upwards, and on the right side, it would continue to decrease but now concaving downwards.
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS